Résumé:

I'll review the phenomenon of wall-crossing in theories with N=2 supersymmetry and its relation to the instanton contributions to the low energy effective actions in gauge and string theories. In the latter case, it is relevant for the description of D-brane instantons. Adding NS5-brane instantons to the story, one arrives to considering certain generalized theta series. I'll derive the properties of these theta series following from the mutual consistency of wall-crossing, D-brane and NS5-brane instantons, and show how these results can be used to get a new type of quantum dilogarithm identities.